If insanity is doing the same thing over and over and expecting a different result, then New York City is certifiably crazy.

Already facing a $5 billion budget gap, unemployment above 10 percent, an ominous spike in crime and other signs of disorder, City Hall is nonetheless expanding its prohibitively expensive services. The added burdens reflect pet projects of politicians, and will do little to improve the quality of life for most New Yorkers, even as they drive up taxes.

Mayor Bloomberg is ready to spend tens of millions on Governors Island, including building a high school accessible only by expensive ferryboat. He took control of the 172-acre property and assumed most of the costs from the state. He also has his eyes on buying Battery Park City from Albany.

He is putting solar panels on the roof of City Hall as part of a $100 million makeover, a project that initially was supposed to cost $62 million.

City Council Speaker Christine Quinn wants to enlarge the recycling program for Earth Day on April 22, putting a new onus on homeowners and businesses and adding more can clutter to congested sidewalks.

The Department of Transportation is opening new fronts in its war on cars, with plans to inflict its traffic-snarling bike-lane madness on fresh neighborhoods.

All these ambitious projects come as the city can’t afford the level of services it already provides. Its $63 billion budget, despite increasing by more than 50 percent under Bloomberg, was recently called “bare bones” by a writer.

As laughable as the concept is, the city is squeezed. It spent the soaring tax revenues from the boom, its debt service is about to double, and it’s now shedding or reducing essential services even as it layers on new responsibilities.

Water rates are going up 12.9 percent and property taxes are sure to follow, but workers on rat patrol have been cut by two-thirds, to just 27 for the whole city, to save $1.5 million. Meanwhile, nearly all municipal workers are getting a 4 percent raise this year.

Amid this largess, there are distinct signs of a fraying quality of life. Some city streets are roller-coaster-like thanks to asphalt that has both deep dips and high bumps. Mounds of trash are visible along highways. Track sections on Metro North have not been cleaned for years. Many subway security cameras don’t work.

Crime is Public Enemy No. 1 and Bloomberg, although he promised not to lay off cops, hasn’t committed to rebuilding the force he let shrink by 15 percent. Murders are up 22.5 percent for the year and shooting incidents last week were up 94 percent over last year.

Supporters of the mayor’s land grab, which includes a state park in Brooklyn, say the state’s even-worse finances are creating “fire-sale prices.” Yet over the long run, the state’s larger tax base makes it better-equipped to assume large financial commitments.

Senior colleges in City University, for example, were taken over by the state to help the city during the fiscal crisis of the ’70s. So the city gets the benefit without the costs. Thus it is odd, and risky, for the city now to be reversing the buyer-seller role on expensive parks it must maintain.

Ah, but City Hall wants to show it has not forgotten the little folk who pay the bills. After a ton of complaints about blaring loudspeakers on open-air tourist buses, the council will require individual headsets for riders.

Hold the applause. The law would cover existing buses in 12 years. Yep, 2022 is when all buses would need to convert to headphones.

Happy Tax Day, New York.

NOW HE’S A CRESCENT LOON

The first time I saw the swirling logo for the Nuclear Security Summit, it looked familiar. I soon figured out what it reminded me of: a crescent moon.

The kind of crescent moon you see on the flags of Muslim countries (from left: Turkey, Algeria, Tunisia and Pakistan).

Indeed, the crescent, often with a single or multiple stars, is the main symbol of Islam. So now there is something like it at an official presidential event, prominently displayed in photographs being beamed around the world.

No, I am not suggesting President Obama is a secret Muslim. But I am certain the crescent-like design of the logo is not a coincidence, especially at an event where Iran’s nuclear ambition and al Qaeda’s search for a bomb are prime topics.

Obama has been open about his aim to improve America’s relations with Muslims. His bowing and apologies are nauseating, but they are consistent with his goal.

And so is having a crescent-like logo at an event attended by Pakistani Prime Minister Yusuf Raza Gilani (above), among others. The Washington Conference Center is plastered with the design, which includes a solid white circle above the arc, all superimposed on a world map.

Consistent also is a report this week that says terms with religious connotations, such as “Islamic extremists” and “jihad,” will no longer be used in National Security Council documents. The Associated Press reports the aim is to emphasize the White House desire to use more sensitive language and broaden the relationship beyond war. The phrase “war on terror” was also dropped.

“Do you want to think about the US as the nation that fights terrorism or the nation you want to do business with? ” Pradeep Ramamurthy, an NSC staffer, told AP. It also reports business leaders from more than 40 countries are coming to Washington for an “entrepreneurship summit” for Muslim businesses.

Notably absent this week is Israeli Prime Minister Benjamin Netanyahu. The deep freeze in his relationship with Obama is a direct casualty of Obama’s courting of Muslims, which includes intense pressure on Israel to make major concessions to Palestinians.

So this is what change looks like.

Slow down, ‘busters!

I enjoy a good political fight on principle, but all the talk about whether Republicans will filibuster Obama’s Su preme Court nominee sounds a tad premature. Here’s an idea: Let’s wait until he actually nominates someone! Geez.

Rise & shine, slackers

My favorite line about Germany’s resistance to bailing out Greece comes from an open letter in the Bild newspaper.

It contrasts supposed German thrift and industry with Greek sloth and corruption, and contains advice neatly summarized: “Get up earlier.”